I will let others focus on the products, I will briefly comment on diet. Check out the healthy eating guidelines - there are adaptations for vegetarians and vegans - note the guidelines are minimums/ maximums/ serving sizes nothing like optimum nutrition. There is also some great advice on vegetarian and vegan websites.
The guideline that covers crisps, snacks, and processed foods like many cereals is for maximum 10% daily calories which is a TINY serving (~200 cals for average female). IME anyone who is off on this is off on many of the others because they don't leave enough calories for a balanced diet. You are probably off on salt, fibre and balance of types of fat for example.
Vegetables/ produce is just one of the guidelines, it is no more important than any other and primarily supplies water soluble vitamins. They are not a good source of essential fatty acids, most minerals or protein, it is also very difficult to eat the rainbow without fruit (blue/ purple family). Key foods for vegetarians to eat frequently include whole eggs, beans, lentils, seeds such as pumpkin and chia, walnuts, unsweetened cocoa.
Veganism is so restrictive compared to what humans evolved eating they need to regiment their meals to have any hope of balance and health. That is not intended as a judgement, most people's interpretation of Paleo is appallingly imbalanced and potentially harmful too.
Without oily fish humans cannot get enough bioavailable vitamin D or long chain omega-3s (DHA/ EPA), without seafood and organ meats usually not enough iron, magnesium, other minerals, certain B group vitamins. Discuss supplementing with your family doctor, registered dietician or other appropriately qualified professional (degree level or higher).
Nutrients scientifically proven relevant in mental health including stress anxiety are covered above - especially magnesium, vitamin D and long chain omega-3s, but also B group vitamins and other minerals. Sugar and processed carbs put the body into a state of stress and are pro inflammatory, absolutely impacts negatively on the skin. Note that in the UK we cannot get enough vitamin D from sunlight between October and April.